1217:
1241:
1229:
1253:
1205:
22:
350:
102:
It is a theoretically interesting measure because it provides different risk values for different individuals whose attitudes toward risk may differ. However, in practice it would be difficult to use since quantifying the risk aversion for an individual is difficult to do. The entropic risk measure
643:
159:
837:
345:{\displaystyle \rho ^{\mathrm {ent} }(X)={\frac {1}{\theta }}\log \left(\mathbb {E} \right)=\sup _{Q\in {\mathcal {M}}_{1}}\left\{E^{Q}-{\frac {1}{\theta }}H(Q|P)\right\}\,}
452:
151:
486:
715:
864:
707:
675:
40:
905:
1041:
884:
975:
462:
58:
1273:
867:
116:
1148:"An ergodic BSDE approach to forward entropic risk measures: representation and large-maturity behavior"
1195:
1080:
1026:
944:
638:{\displaystyle A=\{X\in L^{p}({\mathcal {F}}):E\geq 0\}=\{X\in L^{p}({\mathcal {F}}):E\left\leq 1\}}
686:
358:
130:
912:
832:{\displaystyle \rho _{t}^{\mathrm {ent} }(X)={\frac {1}{\theta }}\log \left(\mathbb {E} \right).}
995:
967:
879:
36:
1067:
1013:
931:
849:
692:
480:
for the entropic risk measure is the set of payoffs with positive expected utility. That is
108:
72:
1095:
959:
651:
8:
104:
88:
1048:
1221:
1179:
1159:
1128:
1110:
96:
1257:
1216:
1132:
971:
960:
1183:
1278:
1169:
1120:
455:
112:
1209:
843:
1245:
477:
1174:
1147:
1042:"Dynamic convex risk measures: time consistency, prudence, and sustainability"
1267:
92:
84:
1233:
80:
1146:
Chong, Wing Fung; Hu, Ying; Liang, Gechun; Zariphopoulou, Thaleia (2019).
1240:
1124:
1164:
1115:
689:
associated with dynamic entropic risk with risk aversion parameter
1252:
91:
function. It is a possible alternative to other risk measures as
866:
is constant through time, and can be computed efficiently using
75:(concerned with mathematical modeling of financial markets), the
1204:
904:
Rudloff, Birgit; Sass, Jorn; Wunderlich, Ralf (July 21, 2008).
127:
The entropic risk measure with the risk aversion parameter
1145:
1094:
Hyndman, Cody; Kratsios, Anastasis; Wang, Renjie (2020).
1193:
903:
852:
718:
695:
654:
489:
361:
162:
133:
994:
Follmer, Hans; Schied, Alexander (October 8, 2008).
962:
Stochastic finance: an introduction in discrete time
906:"Entropic Risk Constraints for Utility Maximization"
1093:
31:
may be too technical for most readers to understand
858:
831:
701:
669:
637:
446:
344:
145:
1265:
680:
250:
993:
957:
1033:
632:
564:
558:
496:
1087:
122:
1173:
1163:
1114:
966:(2 ed.). Walter de Gruyter. p.
958:Föllmer, Hans; Schied, Alexander (2004).
776:
341:
215:
59:Learn how and when to remove this message
43:, without removing the technical details.
868:forward-backwards differential equations
1266:
1039:
989:
987:
885:List of financial performance measures
1139:
677:is the exponential utility function.
41:make it understandable to non-experts
15:
996:"Convex and Coherent Risk Measures"
984:
13:
807:
736:
733:
730:
588:
520:
263:
175:
172:
169:
14:
1290:
471:
1251:
1239:
1227:
1215:
1203:
1096:"The entropic measure transform"
20:
1103:Canadian Journal of Statistics
951:
897:
818:
800:
780:
748:
742:
664:
658:
593:
583:
549:
546:
540:
534:
525:
515:
379:
372:
365:
333:
326:
319:
300:
291:
238:
219:
187:
181:
1:
890:
681:Dynamic entropic risk measure
447:{\displaystyle H(Q|P)=E\left}
117:utility maximization problems
146:{\displaystyle \theta >0}
7:
873:
10:
1295:
103:is the prime example of a
1175:10.1007/s00780-018-0377-3
687:conditional risk measure
111:Given the connection to
87:of the user through the
1274:Financial risk modeling
1152:Finance and Stochastics
859:{\displaystyle \theta }
702:{\displaystyle \theta }
123:Mathematical definition
1075:Cite journal requires
1040:Penner, Irina (2007).
1021:Cite journal requires
939:Cite journal requires
880:Entropic value at risk
860:
833:
703:
671:
639:
448:
346:
147:
861:
834:
704:
672:
640:
449:
347:
148:
83:which depends on the
77:entropic risk measure
73:financial mathematics
850:
716:
693:
670:{\displaystyle u(X)}
652:
487:
359:
160:
131:
115:, it can be used in
918:on October 18, 2012
741:
105:convex risk measure
89:exponential utility
856:
829:
719:
699:
667:
635:
444:
342:
275:
143:
97:expected shortfall
1125:10.1002/cjs.11537
977:978-3-11-018346-7
762:
437:
411:
314:
249:
201:
113:utility functions
69:
68:
61:
1286:
1256:
1255:
1244:
1243:
1232:
1231:
1230:
1220:
1219:
1208:
1207:
1199:
1188:
1187:
1177:
1167:
1143:
1137:
1136:
1118:
1100:
1091:
1085:
1084:
1078:
1073:
1071:
1063:
1061:
1059:
1054:on July 19, 2011
1053:
1047:. Archived from
1046:
1037:
1031:
1030:
1024:
1019:
1017:
1009:
1007:
1005:
1000:
991:
982:
981:
965:
955:
949:
948:
942:
937:
935:
927:
925:
923:
917:
911:. Archived from
910:
901:
865:
863:
862:
857:
846:risk measure if
838:
836:
835:
830:
825:
821:
817:
816:
811:
810:
803:
798:
797:
779:
763:
755:
740:
739:
727:
708:
706:
705:
700:
676:
674:
673:
668:
644:
642:
641:
636:
625:
621:
620:
592:
591:
582:
581:
524:
523:
514:
513:
456:relative entropy
453:
451:
450:
445:
443:
439:
438:
436:
428:
420:
412:
410:
402:
394:
375:
351:
349:
348:
343:
340:
336:
329:
315:
307:
290:
289:
274:
273:
272:
267:
266:
245:
241:
237:
236:
218:
202:
194:
180:
179:
178:
152:
150:
149:
144:
64:
57:
53:
50:
44:
24:
23:
16:
1294:
1293:
1289:
1288:
1287:
1285:
1284:
1283:
1264:
1263:
1262:
1250:
1238:
1228:
1226:
1214:
1202:
1194:
1192:
1191:
1144:
1140:
1098:
1092:
1088:
1076:
1074:
1065:
1064:
1057:
1055:
1051:
1044:
1038:
1034:
1022:
1020:
1011:
1010:
1003:
1001:
998:
992:
985:
978:
956:
952:
940:
938:
929:
928:
921:
919:
915:
908:
902:
898:
893:
876:
851:
848:
847:
844:time consistent
812:
806:
805:
804:
799:
787:
783:
775:
774:
770:
754:
729:
728:
723:
717:
714:
713:
694:
691:
690:
683:
653:
650:
649:
610:
606:
602:
587:
586:
577:
573:
519:
518:
509:
505:
488:
485:
484:
474:
429:
421:
419:
403:
395:
393:
392:
388:
371:
360:
357:
356:
325:
306:
285:
281:
280:
276:
268:
262:
261:
260:
253:
226:
222:
214:
213:
209:
193:
168:
167:
163:
161:
158:
157:
132:
129:
128:
125:
65:
54:
48:
45:
37:help improve it
34:
25:
21:
12:
11:
5:
1292:
1282:
1281:
1276:
1261:
1260:
1248:
1236:
1224:
1212:
1190:
1189:
1138:
1086:
1077:|journal=
1032:
1023:|journal=
983:
976:
950:
941:|journal=
895:
894:
892:
889:
888:
887:
882:
875:
872:
855:
840:
839:
828:
824:
820:
815:
809:
802:
796:
793:
790:
786:
782:
778:
773:
769:
766:
761:
758:
753:
750:
747:
744:
738:
735:
732:
726:
722:
698:
682:
679:
666:
663:
660:
657:
646:
645:
634:
631:
628:
624:
619:
616:
613:
609:
605:
601:
598:
595:
590:
585:
580:
576:
572:
569:
566:
563:
560:
557:
554:
551:
548:
545:
542:
539:
536:
533:
530:
527:
522:
517:
512:
508:
504:
501:
498:
495:
492:
478:acceptance set
473:
472:Acceptance set
470:
442:
435:
432:
427:
424:
418:
415:
409:
406:
401:
398:
391:
387:
384:
381:
378:
374:
370:
367:
364:
353:
352:
339:
335:
332:
328:
324:
321:
318:
313:
310:
305:
302:
299:
296:
293:
288:
284:
279:
271:
265:
259:
256:
252:
248:
244:
240:
235:
232:
229:
225:
221:
217:
212:
208:
205:
200:
197:
192:
189:
186:
183:
177:
174:
171:
166:
153:is defined as
142:
139:
136:
124:
121:
67:
66:
49:September 2010
28:
26:
19:
9:
6:
4:
3:
2:
1291:
1280:
1277:
1275:
1272:
1271:
1269:
1259:
1254:
1249:
1247:
1242:
1237:
1235:
1225:
1223:
1218:
1213:
1211:
1206:
1201:
1200:
1197:
1185:
1181:
1176:
1171:
1166:
1161:
1157:
1153:
1149:
1142:
1134:
1130:
1126:
1122:
1117:
1112:
1108:
1104:
1097:
1090:
1082:
1069:
1050:
1043:
1036:
1028:
1015:
997:
990:
988:
979:
973:
969:
964:
963:
954:
946:
933:
914:
907:
900:
896:
886:
883:
881:
878:
877:
871:
869:
853:
845:
826:
822:
813:
794:
791:
788:
784:
771:
767:
764:
759:
756:
751:
745:
724:
720:
712:
711:
710:
696:
688:
678:
661:
655:
629:
626:
622:
617:
614:
611:
607:
603:
599:
596:
578:
574:
570:
567:
561:
555:
552:
543:
537:
531:
528:
510:
506:
502:
499:
493:
490:
483:
482:
481:
479:
469:
467:
464:
461:
457:
440:
433:
430:
425:
422:
416:
413:
407:
404:
399:
396:
389:
385:
382:
376:
368:
362:
337:
330:
322:
316:
311:
308:
303:
297:
294:
286:
282:
277:
269:
257:
254:
246:
242:
233:
230:
227:
223:
210:
206:
203:
198:
195:
190:
184:
164:
156:
155:
154:
140:
137:
134:
120:
118:
114:
110:
107:which is not
106:
100:
98:
94:
93:value-at-risk
90:
86:
85:risk aversion
82:
78:
74:
63:
60:
52:
42:
38:
32:
29:This article
27:
18:
17:
1155:
1151:
1141:
1106:
1102:
1089:
1068:cite journal
1056:. Retrieved
1049:the original
1035:
1014:cite journal
1002:. Retrieved
961:
953:
932:cite journal
920:. Retrieved
913:the original
899:
841:
709:is given by
684:
647:
475:
465:
459:
354:
126:
101:
81:risk measure
76:
70:
55:
46:
30:
1222:Mathematics
1158:: 239–273.
1058:February 3,
1268:Categories
1258:Technology
1165:1607.02289
1116:1511.06032
1109:: 97–129.
891:References
842:This is a
1133:159089174
854:θ
792:θ
789:−
768:
760:θ
721:ρ
697:θ
627:≤
615:θ
612:−
571:∈
553:≥
503:∈
417:
312:θ
304:−
295:−
258:∈
231:θ
228:−
207:
199:θ
165:ρ
135:θ
109:coherent.
1210:Business
1184:16261697
1004:July 22,
922:July 22,
874:See also
463:<<
1279:Utility
1246:Science
1196:Portals
454:is the
35:Please
1182:
1131:
974:
648:where
355:where
1234:Money
1180:S2CID
1160:arXiv
1129:S2CID
1111:arXiv
1099:(pdf)
1052:(PDF)
1045:(PDF)
999:(PDF)
916:(PDF)
909:(PDF)
79:is a
1081:help
1060:2011
1027:help
1006:2010
972:ISBN
945:help
924:2010
685:The
476:The
138:>
1170:doi
1121:doi
968:174
765:log
458:of
414:log
251:sup
204:log
95:or
71:In
39:to
1270::
1178:.
1168:.
1156:23
1154:.
1150:.
1127:.
1119:.
1107:48
1105:.
1101:.
1072::
1070:}}
1066:{{
1018::
1016:}}
1012:{{
986:^
970:.
936::
934:}}
930:{{
870:.
468:.
119:.
99:.
1198::
1186:.
1172::
1162::
1135:.
1123::
1113::
1083:)
1079:(
1062:.
1029:)
1025:(
1008:.
980:.
947:)
943:(
926:.
827:.
823:)
819:]
814:t
808:F
801:|
795:X
785:e
781:[
777:E
772:(
757:1
752:=
749:)
746:X
743:(
737:t
734:n
731:e
725:t
665:)
662:X
659:(
656:u
633:}
630:1
623:]
618:X
608:e
604:[
600:E
597::
594:)
589:F
584:(
579:p
575:L
568:X
565:{
562:=
559:}
556:0
550:]
547:)
544:X
541:(
538:u
535:[
532:E
529::
526:)
521:F
516:(
511:p
507:L
500:X
497:{
494:=
491:A
466:P
460:Q
441:]
434:P
431:d
426:Q
423:d
408:P
405:d
400:Q
397:d
390:[
386:E
383:=
380:)
377:P
373:|
369:Q
366:(
363:H
338:}
334:)
331:P
327:|
323:Q
320:(
317:H
309:1
301:]
298:X
292:[
287:Q
283:E
278:{
270:1
264:M
255:Q
247:=
243:)
239:]
234:X
224:e
220:[
216:E
211:(
196:1
191:=
188:)
185:X
182:(
176:t
173:n
170:e
141:0
62:)
56:(
51:)
47:(
33:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.